In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 3x-5}\right) \cdot \left( \color{orangered}{ x+6}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{6} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{6} }_{\text{LAST}} = \\ &= 3x^2 + 18x + \left( -5x\right) + \left( -30\right) = \\ &= 3x^2 + 18x + \left( -5x\right) + \left( -30\right) = \\ &= 3x^2+13x-30; \end{aligned} $$

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